English

Find the following integrals: ∫(1-x)xdx - Mathematics

Advertisements
Advertisements

Question

Find the following integrals:

`int(1 - x) sqrtx dx`

Sum
Advertisements

Solution

`int (1 - x) sqrtx  dx`

`I = int (x^(1/2) - x^(3/2))` dx

`I= int x^(1/2)  dx - int x^(3/2)` dx

`I= 2/3  x^(3/2) - 2/5  x^(5/2) + C`

shaalaa.com
  Is there an error in this question or solution?
Chapter 7: Integrals - Exercise 7.1 [Page 299]

APPEARS IN

NCERT Mathematics Part 1 and 2 [English] Class 12
Chapter 7 Integrals
Exercise 7.1 | Q 14 | Page 299

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

 

Find :`int(x^2+x+1)/((x^2+1)(x+2))dx`

 

Find an anti derivative (or integral) of the following function by the method of inspection.

(axe + b)2


Find an antiderivative (or integral) of the following function by the method of inspection.

sin 2x – 4 e3x


Find the following integrals:

`int (4e^(3x) + 1)`


Find the following integrals:

`intx^2 (1 - 1/x^2)dx`


Find the following integrals:

`int (ax^2 + bx + c) dx`


Find the following integrals:

`int(2x^2 + e^x)dx`


Find the following integrals:

`int(sqrtx - 1/sqrtx)^2 dx`


Find the following integrals:

`int (x^3 + 3x + 4)/sqrtx dx`


Find the following integrals:

`intsqrtx( 3x^2 + 2x + 3) dx`


Find the following integrals:

`int(2x - 3cos x + e^x) dx`


Find the following integrals:

`int(2x^2 - 3sinx + 5sqrtx) dx`


Integrate the function:

`1/(x - x^3)`


Integrate the function:

`1/(sqrt(x+a) + sqrt(x+b))`


Integrate the function:

`1/(xsqrt(ax - x^2)) ["Hint : Put x" = a/t]`


Integrate the function:

`1/(x^2(x^4 + 1)^(3/4))`


Integrate the function: 

`1/(x^(1/2) + x^(1/3))  ["Hint:" 1/(x^(1/2) + x^(1/3)) = 1/(x^(1/3)(1+x^(1/6))),  "put x" = t^6]`


Integrate the function:

`(5x)/((x+1)(x^2 +9))`


Integrate the function:

`cos x/sqrt(4 - sin^2 x)`


Integrate the function:

`1/((x^2 + 1)(x^2 + 4))`


Integrate the function:

`cos^3 xe^(log sinx)`


Integrate the function:

f' (ax + b) [f (ax + b)]n


Integrate the function:

`1/sqrt(sin^3 x sin(x + alpha))`


Integrate the function:

`sqrt((1-sqrtx)/(1+sqrtx))`


Integrate the function:

`(x^2 + x + 1)/((x + 1)^2 (x + 2))`


Evaluate `int(x^3+5x^2 + 4x + 1)/x^2  dx`


Find : \[\int\frac{\left( x^2 + 1 \right)\left( x^2 + 4 \right)}{\left( x^2 + 3 \right)\left( x^2 - 5 \right)}dx\] .


The anti derivative of `(sqrt(x) + 1/sqrt(x))` is equals:


`sqrt((10x^9 + 10^x  log e^10)/(x^10 + 10^x)) dx` equals


`int (dx)/(sin^2x cos^2x) dx` equals


`int (sin^2x - cos^2x)/(sin^2x cos^2x) dx` is equal to


`int (xdx)/((x - 1)(x - 2))` equals


`int x^2 e^(x^3) dx` equals


`int sqrt(1 + x^2) dx` is equal to


What is anti derivative of `e^(2x)`


If the normal to the curve y(x) = `int_0^x(2t^2 - 15t + 10)dt` at a point (a, b) is parallel to the line x + 3y = –5, a > 1, then the value of |a + 6b| is equal to ______.


`d/(dx)x^(logx)` = ______.


Anti-derivative of `(tanx - 1)/(tanx + 1)` with respect to x is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×